Question

3. Four runners started running simultaneously from a point on a circular track. They took 200 s, 300 s, 360 s
and 450 s to complete one round. After how much time do they meet at the starting point for the first time?​

Answer 1

➤ Answer

• Time after which all the runners will meet together = 1800 second or 30 minutes.

➤ Given

• Four runners started running simultaneously from a point on a circular track. They took 200 sec, 300 sec, 360 sec, and 450 sec. respectively to complete a round.

➤ To Find

• Time after which they all will meet each other.

➤ Step By Step Explanation

Given that four runners started running simultaneously from a point on a circular track and took 200 s, 300 s, 360 s and 450 s to complete one round. We need to calculate the time after which they all will meet each other.

So let's do it !!

We need to find the L.C.M. of 200, 300, 360 and 450.

➵ Factorization

200 = 2 × 2 × 2 × 5 × 5 => 2³ × 5²

300 = 2 × 2 × 3 × 5 × 5 => 2² × 3 × 5²

360 = 2 × 2 × 2 × 3 × 3 × 5 => 2³ × 3² × 5

450 = 2 × 3 × 3 × 5 × 5 => 2 × 3² × 5²

Here, the height value of 2, 3 and 5 are 2³, 3² and 5².

So L.C.M. will be => 2³ × 3² × 5²

➠ 8 × 9 × 25

➠ 72 × 25

➠ 1800.

➠ Hence, L.C.M. = 1800.

Therefore, the time after which all the runners will meet = 1800 second or 30 minutes.

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